What the Rubik's cube really is It's a device you use to "visit" a larger structure--you see one part at a time--which is composed of the faces of a "solid" with 4 dimensions. It's 3-surface which initially, note that here you decide what the initial condition(s) is, has a choice of visiting one dimension of a graph made out of space and time. This 3-surface is constructed in steps, from the "axiom of choice" which is which dimension to choose to "tile:" the graph. It gets to 3x1 dimensional surfaces in spacetime and starts over. So this means that, after 3x1 surfaces have been "constructed" and used to build a 3-dimensional surface, you have part of a larger graph, and of a larger structure in that case. Abstractly, you now can use the smallest of the "full" group of permutable devices--the Pocket Cube is sliced once in each dimension--to explore the smallest subgroup of a bigger group. Mathematically, there is no reason to not now use the 3-surface as a tile, and so get to larger "dimensions" of the range of this device. The complete map of this group as a poset (graph) is the number of "points" in each of the vertices of a triangle. The triangle looks like one tile, then like two joined along one side, then three, and all their permutations. You eventually get to a tetrahedral subset of tiles you can use as tiles on a 4-dimensional shape. Now spacetime is 4-dimensional because of time being assigned to one of four freely chosen dimensions. I'll let you all work out the remainder of the implications of using 4-dimensional tiles, and so on.
